I did, however, managed to fix the problem.  If only I had actually used
some of my experience from a few years of corporate IT, I might have solved
this problem a lot sooner...

An attempted System Restore this afternoon alerted me that a directory in my
user profile ("Application
Data\Microsoft\SystemCertificates\My\Certificates") was "corrupt and
unreadable", despite chkdsk not being able to find anything in previous
troubleshooting attempts.

The basic step of creating another administrative user and testing from that
account confirmed that the problem was user-related.  I deleted the original
account and user profile, but the "corrupt" directory is still there, and
will probably remain for the rest of the machine's life.

Problem appears to be solved now, however.  I can use Windows Update, all my
Certificates are working properly, and even Norton Antivirus 2002 which gave
a "Permission Denied" error message (seems to use signed components) when
opening, now runs smoothly.

From the number of posts I found on this particular problem (none) I would
guess it is a fairly rare occurence, but creating another user with a fresh
user profile is always a good way to narrow down possible causes of a
problem.